Section 5.2 Binomial Probabilities

2 Features of a Binomial Experiment 1.There are a fixed number of trials, n 2.The n trials are independent and repeated 3.Each trial has only two outcomes: success, S, and Failure, F 4.The probability of success is the same for each trial -Prob. of S = p -Prob. of F = 1 – p = q 5.The goal is to find the probability of r successes out of n trials

3 Ex: 1 3 multiple-choice questions. Each question has 4 choices, only one is correct. You randomly choose an answer for each. a)P(success for each question) = P(failure for each question) = b) List out all the outcomes and their probabilities:

4 Probabilities for Binomial Experiments Formula n: # of trials p: probability of success q: probability of failure r : # of success (random variable of interest) Use it to compute P(1 out of 3 questions correct):

5 Ex: 2 59% of Internet users are worried about their privacy. a) Find P(out of 10 users, 6 are worried). b) Find P(r ≤ 5).

6 Using Binomial Distribution in Calculator 2 nd Vars (distr)  (to find exact # of successes) binompdf(n, p, r) (to find # of success or less) binomcdf(n, p, r) Try: for n = 6 and p = 0.50  P (r = 4) =  P(r  4) =  P(r ≥ 4) =  P(r < 4) =  P(r > 4) =

7 Ex: 3 Seeds of a hybrid tomato have probability 0.70 of germinating. A biologist plants six seeds. a.) P(exactly four seeds will germinate) b.) P(at least four seeds will germinate)

8 Ex: 4 New eye operation known to restore eyesight of 30% of patients. A new technique for this surgery was successful for 4 of the patients. Is the new technique better than the old?

9 Can you English? 4 or more At least 4 No fewer than 4 Not less than or fewer At most 4 No more than 4 Does not exceed More than 4 Exceeds Fewer than 4 Not as large as 4

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